Solution
The stunnel binary listens on these ports and forwards the requests to cpsrvd (the web interface binary). Ensure that it is running.
root@cpdemo [~]# ps wwwaux | grep stunnel
cpanel 25180 0.0 0.2 34572 1364 ? S 03:17 0:00 /usr/bin/stunnel-4.04local /usr/local/cpanel/etc/stunnel/mycabundle/stunnel.conf.run
root 31191 0.0 0.1 4764 672 pts/3 S 15:59 0:00 grep stunnel
root@cpdemo [~]#If it is not running try starting it.
root@cpdemo [~]# ps wwwaux | grep stunnel
root 31228 0.0 0.1 4764 672 pts/3 S 16:00 0:00 grep stunnel
root@cpdemo [~]# /usr/local/cpanel/startstunnel
root@cpdemo [~]# ps wwwaux | grep stunnel
cpanel 31241 0.0 0.3 3696 1656 ? S 16:00 0:00 /usr/bin/stunnel-4.04local /usr/local/cpanel/etc/stunnel/mycabundle/stunnel.conf.run
root 31243 0.0 0.1 4772 672 pts/3 S 16:00 0:00 grep stunnel
root@cpdemo [~]#